This invention relates to a planetary gear assembly which has wide applications as decelerator or accelerator, especially to an asymmetric planetary gear assembly with unified asymmetric planetary gears and an asymmetric internal gear.
A planetary gear assembly comprises a sun gear, three or four planetary gears, an internal gear and a carrier. At six or eight points, planetary gears mesh with a sun gear and an internal gear. The number of engagement points exceeds the number of parts. Therefore, it is difficult to equalize all of transmitting forces acting upon the engagement points. Even very small errors are likely to make the transmitting forces uneven. Uneven engagement means a too deep engagement on one hand and a too shallow engagement on the other hand. Heightening the accuracy of finishing of the gears does not necessarily lead to a fruitful result. Deep engagement between the planetary gears and the sun gear or the internal gear causes increased vibration, noise and energy loss.
Ordinary planetary gear assemblies utilize simple gears without side discs. To solve the problem of uneven engagement, improved planetary gear assemblies having planetary gears with discs and an internal gear with rings on both sides or on one side thereof, have been proposed. In such an improved assembly, the diameters of the planetary discs or the internal rings are equal to the diameters of pitch circles of the planetary gears or the internal gear, respectively.
A pitch circle is a circle which properly represents the size of a gear. Roughly speaking, the pitch circle is a circle obtained by connecting middle points of the gear teeth between the tooth roots and the tooth edges. In other words, if two engaging gears would be replaced by friction wheels (e.g. discs or rings) without changing the rotation ratio or distance between the gear shafts, the friction wheels would represent the size of the pitch circles. Although it is rather difficult to define the pitch circle, the pitch circle has a definite significance. One conventional method of gear design is based on a "module system." A module is the ratio of pitch diameter to the number of gear teeth. The module of a gear is designated by "m". The number of gear teeth is designated by "Z". The diameter D of the pitch circle is given by EQU D=m Z (1) EQU Thus, m=D/Z (1b)
The module "m" is a parameter which represents the thickness of a tooth. Two gears with different modules "m" or different pressure angles ".alpha." cannot mesh together.
A circle which connects the tooth edges of a gear is called a tooth edge circle. Although a basic gear tooth profile can be varied in the module system, one conventional tooth profile standard sets the distance between the pitch circle and the tooth edge circle at 1 module. Therefore, in the case of outer-toothed gears, the tooth edge circle is 1 module greater than the pitch circle in radius. In the case of inner-toothed gears, the tooth edge circle is 1 module smaller than the pitch circle in radius.
Namely, the diameter E of the tooth edge circle is given by EQU E=m(Z.+-.2) (2)
where outer-toothed gears employ the upper sign and inner-toothed gears employ the lower sign.
A circle which connects tooth roots of a gear is called a tooth root circle. The conventional tooth profile standard mentioned above sets the distance between the pitch circle and the tooth root circle at 1.25 modules. In the case of outer-toothed gears, the tooth root circle is 1.25 modules smaller than the pitch circle in radius. In the case of inner-toothed gears, the tooth root circle is 1.25 modules bigger than the pitch circle in radius.
Namely, the diameter F of a tooth root circle is given by EQU F I m (Z.+-.2.5) (3)
where outer-toothed gears employ the upper sign and inner-toothed gears employ the lower sign.
If discs or rings whose diameters are equal to that of the pitch circles are fitted on the sides of the gears, radial forces are transmitted through the pitch discs or pitch rings.
Therefore, in the planetary gear assemblies with pitch discs and rings, even if the sun gear shaft is eccentric, the planetary shafts deviate from exact points on the carrier or the output shaft is eccentric, the gears don't excessively mesh with each other, because excess radial displacements are forbidden by the pitch discs and rings.
There is an important reason why the discs or rings fitted on the sides of the gears must be the same diameter as the pitch circles or pitch rings. As mentioned before, if two engaging gears would be replaced by two contacting friction wheels, only friction wheels with pitch circle diameters the same as the replaced gears would give the same rotation ratio, without changing the distance between shafts. Therefore, when two gears having pitch discs or pitch rings on their sides are meshed with each other, no slipping occurs between the pitch rings or pitch discs.
A lot of planetary gear assemblies with pitch discs or pitch rings have been invented so far. Such planetary gear assemblies are now called a "pitch circle type", examples of which can be seen in the following references.
(1) U.S. Pat. No. 3,293,928 (Dec. 27, 1966) PA1 (2) U.S. Pat. No. 3,548,673 (Dec. 22, 1970) PA1 (3) U.S. Pat. No. 3,789,700 (Feb. 5, 1974) PA1 (4) U.S. Pat. No. 1,970,251 (Aug. 14, 1934) PA1 (5) U.S. Pat. No. 1,586,309 (May 25, 1926) PA1 (6) U.S. Pat. No. 3,216,270 (Nov. 9, 1965) PA1 (7) German Patent Publication 2,032,723 (Apr. 13, 1972) PA1 (8) British Patent 1,107,062 (Jun. 16, 1965) PA1 (9) U.S. Pat. No. 3,330,171 (Jul. 11, 1967) PA1 (10) German patent 444,697 (May 24, 1927) PA1 (11) U.S. Pat. No. 1,425,430 (Aug. 8, 1922) PA1 (12) Japanese Utility Model Publication No. 30-16918 (Nov. 18, 1955) PA1 (13) Japanese Patent Publication No. 54-17111 (Jun. 27, 1979) PA1 (14) Japanese Utility Model Publication No. 57-41486 (Sep. 11, 1982) PA1 (15) Japanese Patent Publication No. 57-48702 (Oct. 18, 1982) PA1 (16) U.S. Pat. No. 4,109,545 (Aug. 29, 1978) PA1 (1) Japanese Patent Application No. 58-143466 Filed on Aug. 5, 1983 PA1 (2) Japanese Patent Application No. 59-106976 Filed on May 26, 1984 PA1 (3) Japanese Patent Application No. 59-150145 Filed on Jul. 19, 1984 PA1 (Equivalent Foreign Patents; U.S. Pat. No. 4,617,839, Australian Patent 553,968)
The uniqueness of the pitch circle type of planetary gear assembly will now be explained. The pitch circle is a unique circle for every gear. Only gears having pitch discs or rings don't slip each other at the contact points, because line velocities of the discs and rings are equal at the contact points.
If engaging gears would have contacting side discs or rings with diameters other than the pitch circle, the line velocities of the discs or rings would be different at the contact points.
If the line velocities of the side discs or rings are equal, no slipping occurs at the contact points. If the line velocities of the discs or rings are not equal, slipping does occur at the contact points. Slipping between side discs and rings causes energy losses.
It is conventionally thought that the pitch circle type planetary gear assembly should have excellent energy loss characteristics, since no slipping occurs at the contact points. This is an important matter which will be explained in more detail.
It is assumed that an outer-toothed gear P with a tooth number Z.sub.p meshes with an inner-toothed gear I with a tooth number Z.sub.1 at a point C. The module of the gears is denoted by "m". Centers of the outer-toothed gear P and the inner-toothed gear I are designated by "O.sub.p " and "O.sub.1 ", respectively.
The pitch diameter D, of the gear P is defined by EQU D.sub.p =m Z.sub.p ( 4)
The pitch diameter D of the gear I is defined by EQU D.sub.1 =m Z.sub.1 ( 5)
When the two gears mesh each other, the contact point C must lie on both pitch circles of the gears. Namely, the two pitch circles of the two gears contact each other at the contact point C.
The distances O.sub.p C and O.sub.1 C between the contact point C and the centers O.sub.p and O.sub.1 are expressed by EQU O.sub.p C=D.sub.p / 2 (6) EQU O.sub.1 C=D.sub.1 / 2 (7)
Because the two pitch circles contact at the contact point C, the three points O.sub.p, O.sub.1, and C must lie on the same straight line.
The distances O.sub.1 O.sub.p between the centers of the gears is calculated by EQU O.sub.1 O.sub.p =(D.sub.1 -D.sub.p) / 2 (8) EQU m(Z.sub.1 -Z.sub.p) / 2 (9)
The angular velocities of the outer-toothed gear P and the inner-toothed gear I are denoted by .OMEGA..sub.p and .OMEGA..sub.1, respectively. Here, counterclockwise rotation is determined to be positive regarding angular velocity.
Because the line velocities are equal at the contact point, the products of angular velocity and tooth number are equal. EQU Z.sub.p .OMEGA..sub.p =Z.sub.1 .OMEGA..sub.1 ( 10)
This equation means that angular velocity is inversely proportional to tooth number. This is a well-known relation.
If the outer-toothed gear P has side discs whose outer radius is R.sub.p and the inner-toothed gear I has side rings whose inner radius is R.sub.1 and the side discs and rings contact each other, the difference of radius ##EQU1##
The line velocity of the disc R.sub.p at the contact point is R.sub.p .OMEGA..sub.p. The line velocity of the ring R.sub.1 at the contact point is R.sub.1 .OMEGA..sub.1. The difference W between the line velocities V.sub.p of the disc R.sub.p and V.sub.1 of the ring R.sub.1 is calculated by ##EQU2##
If R.sub.p is a pitch disc and R.sub.1 is a pitch ring, R.sub.p =D.sub.p /2 and R.sub.1 =D.sub.1 /2. Thus, the difference w of the line velocities is zero.
Otherwise, it is assumed that R.sub.p is greater than the pitch disc by .DELTA. and R.sub.1 is smaller than the pitch ring by .DELTA.. ##EQU3##
The reason why both deviations have plus sign in Eq. (15) and (16) is that the contact condition of Eq. (11) must be kept.
Substituting Eq. (15) and (16) into Eq. (14), we obtain EQU W=(D.sub.p .OMEGA..sub.p -D.sub.1 .OMEGA..sub.1)/2+.DELTA.(.OMEGA..sub.p -.OMEGA..sub.1) (17)
From Eq. (4), Eq. (5) and Eq. (10), the first term of Eq. (17) becomes zero. Then the difference W of line velocities is EQU W=.DELTA.(.OMEGA..sub.p .OMEGA..sub.1) (18)
When R.sub.p and R.sub.1 are a pitch disc and a pitch ring, the difference W is zero, because .DELTA.=0. But if .DELTA. is not zero, W is not zero. In this case, the line velocity V.sub.p of the disc R.sub.p differs from the line velocity V.sub.1 of the ring R.sub.1 at the contact point C.
To equalize the line velocities of the two friction wheels (disc or ring) at the contact point, the diameters of the friction wheels must be equal to that of the pitch circles. If the line velocities are different, the friction wheels must slip at the contact point. Slipping causes increased energy losses and noise. If the friction force is too large, the rotation of gears would be stopped, because the difference of line velocities is likely to damp the rotation of the counterpart wheels.
The above is the conventional thought about gear engagement. Therefore, conventional side friction wheels (discs or rings) have been pitch circle wheels without exception. FIG. 8 (PRIOR ART) shows an example of a planetary gear (80) with side discs (81) having the same diameter as the pitch circle (82).
However, side discs and rings do not always contact each other. Sometimes the side discs and rings are separated. The time length of separation can be longer than the time length of contact.
It was thought that the discs or rings did not necessarily need to be pitch circle ones. Thus, a new type of planetary gear assembly was invented which is called a "tooth edge circle type." It is disclosed in Japanese Patent Application No. 56-193113, Japanese Patent Laying Open 58-94656 (Laid open on June 4, 1983).
FIG. 7 shows a planetary gear (70) of a tooth edge circle type. The gear (70) has two discs (71) on both sides and a pitch circle (72). These side discs (71) are not pitch discs. But they are larger in diameter than the tooth edge circle (73) of the gear (70). As a counterpart, an internal gear has two side inner cylindrical surfaces. The inner surfaces are bigger than the tooth root circle of the gear. In the tooth edge circle type, an internal gear can be formed in a single body, because side inner cylindrical surfaces are bigger than the tooth root circle. Then the tooth edge circle type has an advantage in that the number of parts can be reduced.
At first, it was considered doubtful whether such a planetary gear assembly could really rotate, because both planetary side discs and internal side surfaces deviated from the pitch circles. Then such tooth edge circle type gears were constructed and inspected to determine whether they could rotate. Indeed, the planetary gear assembly rotated smoothly.
There had been one anxiety. In the tooth edge type of planetary gear assembly having non-pitch circle discs or rings, the line velocities of the discs or rings were different and, it was believed that the discs or rings would produce a braking effect on their counterparts at the contact point. But the test results clearly denied such anxiety. The tooth edge type of gear rotated smoothly without energy loss.
It was concluded that the smooth rotation perhaps derives from the fact that the disc surface of the planetary gear and the inner cylindrical surfaces of the internal gear do not always contact nor slip each other.
Two modified planetary gear assemblies have been mentioned so far, pitch circle type and tooth edge circle type. Both pitch circle type and tooth edge circle type are plane-symmetric regarding the central plane. In the case of the tooth edge circle type, a planetary gear has two equivalent discs on both sides.
On the contrary, another new asymmetric type of planetary gear assembly is not symmetric with regard to the central plane of gears. The asymmetric planetary gear has been disclosed in the following references:
Japanese Patent Laying Open No. 60-34553 Laid Open on Feb. 22, 1985 PA2 Japanese Patent Laying Open No. 61-252845 Laid Open on Dec. 13, 1985 PA2 Japanese Patent Laying Open No. 61-27337 Laid Open on Feb. 6, 1986
The new planetary gear assembly provides a disc on only one side of the planetary gear. It is rather imperfect.
Other new planetary gear assemblies provide two discs on both sides of the planetary gear. One side disc is larger in diameter than the tooth edge circle. Another side disc is smaller in diameter than the tooth root circle. Correspondingly, an internal gear is provided with two side inner cylindrical surfaces. One inner cylindrical surface is bigger in diameter than the tooth root circle of the internal gear. Another inner cylindrical surface is smaller in diameter than the tooth edge circle of the internal gear. The side discs of the planetary gears contact with and roll on the side inner cylindrical surfaces.
The line velocities of the side disc planetary gears are different from the line velocities of the inner cylindrical surfaces of the internal gear. It is not a simple difference. The differences of line velocities between the discs and inner surfaces are in reverse relation on a right hand side and a left hand side. For example, if the line velocity of the discs is bigger than that of the inner surface on the right hand side, the line velocity of the discs is smaller than that of the inner surface on the left hand side.
It was doubtful whether such an asymmetric planetary gear assembly could rotate without friction loss.
In practice, an asymmetric planetary gear assembly was constructed and tested. The asymmetric planetary gear assembly rotated smoothly, against expectation.
In the case of the asymmetric type, a sun gear shaft can be inserted from a vacant side after construction of the gear assembly. Further, the sun gear has a side cylindrical part. The side cylindrical part determines the proper position of the sun gear among the several planetary gears because the sun cylindrical part contacts all the planetary discs. Thus, the sun cylindrical part prevents an abnormal fitting of the sun gear with the planetary gears.
The asymmetric type has such advantages. A planetary gear includes three parts, a gear and two side discs. There are some clearances among the three parts. Owing to these clearances, the three parts are allowed free relative rotation.
Although the differences of the line velocities between the planetary discs and the inner cylindrical surface are different on the right hand side and left hand side, free relative rotation of the three parts of the planetary gear enables the asymmetric planetary gear assembly to rotate freely.
The above-mentioned asymmetric type as well as the tooth edge type are provided with the planetary gears having a central gear and two side discs. The fact that a planetary gear has three parts increases the cost for the parts and construction.
If the planetary gear can be made in a single body, the cost for the parts and construction would be decreased.
Because three or four planetary gears are used in an assembly, the cost reduction by reducing the number of parts would be multiplied and would be desirable.
In the pitch circle type, a conventional planetary gear has a middle gear and two side pitch discs. However, such a simplified planetary gear would be unbalanced.
In the tooth edge circle type, a conventional planetary gear has three parts without fail.
In these types, a planetary gear cannot be made in a single body. This fact increases part and construction cost.
Accordingly, it is a primary object of this invention to provide a planetary gear assembly including planetary gears which have a gear part and side disc parts unified in a body. A unified planetary gear would reduce part and construction cost.
To unify the three parts of the planetary gear, the planetary gears and the internal gear must be asymmetric with regard to the central plane vertical to the gear axis.
The prior asymmetric planetary gears disclosed by Japanese Patent Laying Open No. 60-252845 and No. 61-27337, were asymmetric in order to insert a sun gear unified with a shaft among the planetary gears after construction.
However, symmetry of the gears of this invention does not aim to inserting a sun gear shaft after construction. But an asymmetric shape of gears are an inevitable result of unifying a planetary gear part and two disc parts in a body. The asymmetry of this invention has no connection with the possibility of inserting a sun gear shaft.
It is a further object of this invention to provide a planetary gear assembly with a high efficiency of torque transmission.
Another object of this invention is to provide an improved planetary gear assembly with decreased noise and vibration generation.